Organizing posts.

Well, by default the home-page is listing an X number of posts (latest posts). The other pages are just pages and are not related to posts.

If you would like to add some navigation in form of your current categories, I suggest you add the Categories widget to your sidebar ??

My guess is that the pages on top are normal pages, and not the current categories (therefor you won’t see any posts in them, they’re just pages). If you want to add your categories in that part of your theme, you should edit the theme itself.

So I am to understand that there isn’t a way to publish a post to a recently created page?

No, unless you change the templates (add the right code to it to display the posts from the category you want), or add a php plugin (like Exec-php) which allows you to add PHP code to your pages (that’ll actually execute). But then you’ll still have to know the correct function and variables to use.